M. Grazia Pittau

A Default Prior Distribution for Logistic and Other Regression Models

We propose a new prior distribution for classical (non-hierarchical) logistic regression models, constructed by first scaling all nonbinary variables to have mean 0 and standard deviation 0.5, and then placing independent Student-t prior distributions on the coefficients. As a default choice, we recommend the Cauchy distribution with center 0 and scale 2.5, which in the simplest setting is a longer-tailed version of the distribution attained by assuming one-half additional success and one-half additional failure in a logistic regression. We implement a procedure to fit generalized linear models in R with this prior distribution by incorporating an approximate EM algorithm into the usual iteratively weighted least squares. We illustrate with several examples, including a series of logistic regressions predicting voting preferences, an imputation model for a public health data set, and a hierarchical logistic regression in epidemiology. We recommend this default prior distribution for routine applied use. It has the advantage of always giving answers, even when there is complete separation in logistic regression (a common problem, even when the sample size is large and the number of predictors is small) and also automatically applying more shrinkage to higher-order interactions. This can be useful in routine data analysis as well as in automated procedures such as chained equations for missing-data imputation.

Income distribution in Italy: A nonparametric analysis

Using kernel density estimation, this paper describes the real income distribution and how it evolved over time in Italy. Data are cross-sectional samples from the population of Italian households during the period 1987–1998. A non parametric test is applied to asses whether the observed changes in the distribution are statistically significant, while the presence of more than one mode in the distributions is investigated by a bootstrap test. Empirical results show that the Italian income distribution significantly changed over time, accompanied by a decreasing inequality pattern until 1991 and a subsequent rise. No marked income gains were perceived, while the real “losers” of the decade seem to be households in the middle-upper income range.

Mixture models and convergence clubs

In this paper we argue that modelling the cross-country distribution of per capita income as a mixture distribution provides a natural framework for the detection of convergence clubs. The framework yields tests for the number of component distributions that are likely to have more power than bump hunting tests and includes a natural method of assessing the cross-component immobility necessary to imply a correspondence between components and convergence clubs. Applying the mixture approach to cross-country per capita income data for the period 1960 to 2000 we find evidence of three component densities in each of the nine years that we examine. We find little cross-component mobility and so interpret the multiple mixture components as representing convergence clubs. We document a pronounced tendency for the strength of the bonds between countries and clubs to increase. We show that the well-known hollowing out of the middle of the distribution is largely attributable to the increased concentration of the rich countries around their component means. This increased concentration as well as that of the poor countries around their component mean produces a rise in polarization in the distribution over the sample period.

The Make-Up of a Regression Coefficient: An Application to Gender

In this paper we illustrate the potential use of an old/new methodology which combines the use of concentration curves in order to investigate the components that make up a regression coefficient. The illustration is based on examining gender differences in the effect of age on labor market participation in Italy. Women participation rate is substantially lower than men, but their age profile is similar. The most striking difference is in terms of hours of work: while Italian men increase their work effort until the age of 35, Italian women reduce it until the age of 39. These results do not differ substantially when we split the working population into employed and self-employed. Earnings increase with age for both men and women, however the local regression coefficient is negative for Italian women in the age of 38–42. This evidence is accentuated when we focus on the employees.

Does Regional Cost-of-Living Reshuffle Italian Income Distribution?

This paper examines how spatial price differentials affect income distribution in Italy. The distribution of household income is “reshuffled” after controlling for the purchasing power of households residents in different regions, but only when housing price variations are included in the PPP index. Poor households living in Southern Italy alleviate their relative condition, but concentration of poverty still holds in the Southern part of the country.

Measuring the Middle Class in Kazakhstan : A Subjective Approach

This paper proposes a model-based approach to estimate income boundaries for identifying the middle class in Kazakhstan over 2003-15. The approach exploits the subjective evaluation of Kazakhstan households about their social status, relating self-declared social class membership to income. Income data come from the Kazakhstan Household Budget Survey, which also includes a specific module on quality of life and perceived social status. As social status is intrinsically an ordinal response, the paper estimates a proportional odds model with income as the key explanatory variable. Although other factors influence the self-perception of being in the middle class, income is by far the most important determinant. Benchmarking on 2013, the estimated middle class lower bound is

A Tale of Two Worlds: Willingness to Redistribute in Europe and in the U.S.

14 at 2011 purchasing power parity and the upper bound is

Fitting a fuzzy consensus partition to a set of partitions to analyze the modern economic growth across countries

52. The Kazakhstan middle class has increased massively in size and income concentration. The increase is essentially due to a growth effect rather than a redistributive cause.

Economic Disparities and Life Satisfaction in European Regions

Our paper empirically evaluates the magnitude of the disparities across European countries and American divisions in the demand for redistribution in the 2000s. We identify which are the individual characteristics and the contextual variables that contribute the most in predicting the observed different support for redistribution. We model demand for redistribution in a multilevel framework that provides a natural and suitable model for accounting different levels of variation, at individual level and at macro level, simultaneously.

Metodi non parametrici nell'analisi della distribuzione del reddito: problemi empirici ed aspetti metodologici

In this paper the economic development of a set of countries from 1975 to 1995 is estimated by considering different variables, reflecting the degree of the Modem Economic Growth, MEG, that is the economic progress of nations as a whole (Kuznets, 1966). In each year of the analysis (h=1,…r) the MEG is investigated by a fuzzy partition of then countries measured by four macroeconomic indicators. Since the objective of this paper is to catch the different aspects of the MEG not only in each year but also over the entire period, a new model is developed. In particular, according to the least-squares fitting criterion, aconsensus fuzzy partition is introduced for fitting the best fuzzy partition toP. beingP the set ofr fuzzy partitions of the same set of then countries. The results show that the empirical MEG is well approximated by two groups in 1975, 1980 and 1985, representing two well separated clusters of underdeveloped and developed countries. In 1990, these two clusters tend to split into three groups and the third group includes the countries characterised by a marked acceleration in the rate of output growth. The optimal number of clusters is determined by generalising the empirical test proposed by Calinski and Harabasz (1974) to detect the optimal number of classes of a crisp partition.